Max7219 has 16 dimming levels for the matrix as a whole. You can't dim individual leds, only switch them on/off.
Tlc5940 has 4,000 dimming levels and each individual led can be individually dimmed. But the thing is, each tlc chip, used by itself, can only control 16 LEDs, versus 64 LEDs with the max chip. So you would need 12 tlc chips in total rather than 3 max chips. Unless, that is, you use the tlc chips as part of a multiplexing circuit. If you do that, you probably only need 2 tlc chips, plus some kind of chip to drive the anodes such as mic5891. But this will make the software side more complex. The Arduino would have to run the multiplexing as well as handling the animations. That's all perfectly possible, but harder for a beginner. By contrast, the max chips take care of the multiplexing themselves, leaving the Arduino free to handle the animation.